I notice this SE has a generic "comment bubble" icon with "cc" in it. What's that stand for? Closed Captioning? [joke]
I think this baby would look sweet as the icon for this StackExchange:
Why not use it?
All StackExchange sites in Beta use a standard theme. If you explore the newest sites in the network, you'll notice that the beta sites all use this theme, with the exception of the language-specific branches of StackOverflow.
This helps distinguish the beta sites, those whose scopes are being adjusted and whose cultures are being formed, from the larger and more-established stacks. It also saves StackExchange from expending resources on customization on sites for which it is unclear when, or even if, graduation will come. When that day does come, the designers will go to town.
The quickest and easiest answer to your question is "that's CiviCRM's logo; they own it, we don't." And choster is generally right; most of our new/beta sites use the same generic theme.
There are exceptions, though. I don't remember the details offhand, but Craft CMS Stack Exchange has an icon that's sort of a hybrid of our rectangular speech bubble thing and Craft's distinctive letter C and shade of red. If CiviCRM would be interested in doing something similar, we could definitely look into this more closely.
Thanks to the support and logo-generosity of the CiviCRM team, this is now implemented!